Question 1

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x)shown.The particle:

Accepted Answer

A) moves to a point to the left of x = e, stops and remains at rest 
B) moves to the point x = e, then moves to the left 
C) moves to infinity at varying speed 
D) moves to x = b where it remains at rest 
E) moves to x = e and then to x = d, where it remains at rest 
A) moves to a point to the left of x = e, stops and remains at rest 
B) moves to the point x = e, then moves to the left 
C) moves to infinity at varying speed 
D) moves to x = b where it remains at rest 
E) moves to x = e and then to x = d, where it remains at rest B

Question 2

A 700-N man jumps out of a window into a fire net 10 m below.The net stretches 2 m before bringing the man to rest and tossing him back into the air.The maximum potential energy of the net, compared to its unstretched potential energy, is:

Accepted Answer

A) 300 J 
B) 710 J 
C) 850 J 
D) 7000 J 
E) 8400 J 
A) 300 J 
B) 710 J 
C) 850 J 
D) 7000 J 
E) 8400 J E

Question 3

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s.The greatest speed of the block is:

Accepted Answer

A) 0.32 m/s 
B) 0.55 m/s 
C) 0.71 m/s 
D) 0.87 m/s 
E) 0.93 m/s 
A) 0.32 m/s 
B) 0.55 m/s 
C) 0.71 m/s 
D) 0.87 m/s 
E) 0.93 m/s C

Question 4

An elevator is rising at constant speed.Consider the following statements: I.the upward cable force is constant
II.the kinetic energy of the elevator is constant
III.the gravitational potential energy of the Earth-elevator system is constant
IV.the acceleration of the elevator is zero
V.the mechanical energy of the Earth-elevator system is constant

Accepted Answer

A) all five are true 
B) only II and V are true 
C) only IV and V are true 
D) all but III are true 
E) only I, II, and IV are true 
A) all five are true 
B) only II and V are true 
C) only IV and V are true 
D) all but III are true 
E) only I, II, and IV are true

Question 5

A golf ball is struck by a golf club and falls on a green eight feet above the tee.The potential energy of the Earth-ball system is greatest:

Accepted Answer

A) just before the ball is struck 
B) just after the ball is struck 
C) just after the ball lands on the green 
D) when the ball comes to rest on the green 
E) when the ball reaches the highest point in its flight 
A) just before the ball is struck 
B) just after the ball is struck 
C) just after the ball lands on the green 
D) when the ball comes to rest on the green 
E) when the ball reaches the highest point in its flight

Question 6

The potential energy of a particle moving along the x axis is given by U(x)= (8.0 J/m2)x2 + (2.0 J/m4)x4.
If the total mechanical energy is 9.0 J, the limits of motion are:

Accepted Answer

A) -0.96 m; +0.96 m 
B) -2.2 m; +2.2 m 
C) -1.6 m; +1.6 m 
D) -0.96 m; +2.2 m 
E) -0.96 m; +1.6 m 
A) -0.96 m; +0.96 m 
B) -2.2 m; +2.2 m 
C) -1.6 m; +1.6 m 
D) -0.96 m; +2.2 m 
E) -0.96 m; +1.6 m

Question 7

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis.The points of stable equilibrium are:

Accepted Answer

A) only a 
B) only b 
C) only c 
D) only d 
E) b and d 
A) only a 
B) only b 
C) only c 
D) only d 
E) b and d

Question 8

A 6.0-kg block is released from rest 80 m above the ground.When it has fallen 60 m its kinetic energy is approximately:

Accepted Answer

A) 4700 J 
B) 3500 J 
C) 1200 J 
D) 120 J 
E) 60 J 
A) 4700 J 
B) 3500 J 
C) 1200 J 
D) 120 J 
E) 60 J

Question 9

The graphs below show the magnitude of the force on a particle as the particle moves along the positive x axis from the origin to x = x1.The force is parallel to the x axis and is conservative.The maximum magnitude F1 has the same value for all graphs.Rank the situations according to the change in the potential energy associated with the force, least (or most negative)to greatest (or most positive).

Accepted Answer

A) 3, 1, 2 
B) 1, 3, 2 
C) 2, 3, 1 
D) 3, 2, 1 
E) 2, 1, 3 
A) 3, 1, 2 
B) 1, 3, 2 
C) 2, 3, 1 
D) 3, 2, 1 
E) 2, 1, 3

Question 10

The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing?

Accepted Answer

A) 2.0 m/s 
B) 2.2 m/s 
C) 3.1 m/s 
D) 4.4 m/s 
E) 6.0 m/s 
A) 2.0 m/s 
B) 2.2 m/s 
C) 3.1 m/s 
D) 4.4 m/s 
E) 6.0 m/s

Question 11

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis.The points of unstable equilibrium are:

Accepted Answer

A) only a 
B) only b 
C) only c 
D) only d 
E) b and d 
A) only a 
B) only b 
C) only c 
D) only d 
E) b and d

Question 12

Two particles interact by conservative forces.In addition, an external force acts on each particle.They complete round trips, ending at the points where they started.Which of the following must have the same values at the beginning and end of this trip?

Accepted Answer

A) a total kinetic energy of the two-particle system 
B) the potential energy of the two-particle system 
C) the mechanical energy of the two-particle system 
D) the total linear momentum of the two-particle system 
E) none of the above 
A) a total kinetic energy of the two-particle system 
B) the potential energy of the two-particle system 
C) the mechanical energy of the two-particle system 
D) the total linear momentum of the two-particle system 
E) none of the above

Question 13

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)=(8.0 J/m2)x2 + (2.0 J/m4)x4.
When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s.It next stops momentarily to turn around at x =

Accepted Answer

A) 0 m 
B) -1.1 m 
C) 1.1 m 
D) -2.3 m 
E) 2.3 m 
A) 0 m 
B) -1.1 m 
C) 1.1 m 
D) -2.3 m 
E) 2.3 m

Question 14

A stationary mass m = 1.3 kg is hanging from a spring of spring constant k = 1200 N/m.You raise the mass a distance of 10 cm above its equilibrium position in a time of 1.4 s.What was the average power expended?

Accepted Answer

A) 0.93 W 
B) 4.3 W 
C) 5.2 W 
D) 8.6 W 
E) 10.2 W 
A) 0.93 W 
B) 4.3 W 
C) 5.2 W 
D) 8.6 W 
E) 10.2 W

Question 15

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below.They all start with the same speed and continue to move until brought to rest by friction.Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.

Accepted Answer

A) The same for all cases 
B) 1, 2, 3 
C) 1, then 2 and 3 tie 
D) 3, 1, 2 
E) 2, 1, 3 
A) The same for all cases 
B) 1, 2, 3 
C) 1, then 2 and 3 tie 
D) 3, 1, 2 
E) 2, 1, 3

Question 16

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m3)x3.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

Accepted Answer

A) (2 J/m4)x4 
B) (-2 J/m4)x4 
C) (24 J/m2)x2 
D) (-24 J/m2)x2 
E) 5 J - (2 J/m4)x4 
A) (2 J/m4)x4 
B) (-2 J/m4)x4 
C) (24 J/m2)x2 
D) (-24 J/m2)x2 
E) 5 J - (2 J/m4)x4

Question 17

A stationary mass m = 1.3 kg is hanging from a spring of spring constant k = 1200 N/m.You raise the mass a distance of 10 cm above its equilibrium position.How much has the potential energy of the mass-spring system changed?

Accepted Answer

A) 1.3 J 
B) 6.0 J 
C) 7.3 J 
D) 12 J 
E) 13 J 
A) 1.3 J 
B) 6.0 J 
C) 7.3 J 
D) 12 J 
E) 13 J

Question 18

A small object slides along the frictionless loop-the-loop with a diameter of 3 m.What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

Accepted Answer

A) 1.9 m/s 
B) 3.8 m/s 
C) 5.4 m/s 
D) 15 m/s 
E) 29 m/s 
A) 1.9 m/s 
B) 3.8 m/s 
C) 5.4 m/s 
D) 15 m/s 
E) 29 m/s

Question 19

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)= (8.0 J/m2)x2 − (2.0 J/m4)x4.When the particle is at x = 1.0 m the magnitude of its acceleration is:

Accepted Answer

A) 0 m/s2 
B) -8 m/s2 
C) 8 m/s2 
D) -40 m/s2 
E) 40 m/s2 
A) 0 m/s2 
B) -8 m/s2 
C) 8 m/s2 
D) -40 m/s2 
E) 40 m/s2

Question 20

Objects A and B interact with each other via both conservative and nonconservative forces.Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the internal energy.If no external agent does work on the objects then:

Accepted Answer

A) KA + U is conserved 
B) KA + U + Eint is conserved 
C) KA + KB + Eint is conserved 
D) KA + KB + U is conserved 
E) KA + KB + U + Eint is conserved 
A) KA + U is conserved 
B) KA + U + Eint is conserved 
C) KA + KB + Eint is conserved 
D) KA + KB + U is conserved 
E) KA + KB + U + Eint is conserved

Exam 8: Potential Energy and Conservation of Energy

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x)shown.The particle:

A 700-N man jumps out of a window into a fire net 10 m below.The net stretches 2 m before bringing the man to rest and tossing him back into the air.The maximum potential energy of the net, compared to its unstretched potential energy, is:

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface.When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s.The greatest speed of the block is:

A golf ball is struck by a golf club and falls on a green eight feet above the tee.The potential energy of the Earth-ball system is greatest:

The potential energy of a particle moving along the x axis is given by U(x)= (8.0 J/m2)x2 + (2.0 J/m4)x4. If the total mechanical energy is 9.0 J, the limits of motion are:

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis.The points of stable equilibrium are:

A 6.0-kg block is released from rest 80 m above the ground.When it has fallen 60 m its kinetic energy is approximately:

The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing?

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis.The points of unstable equilibrium are:

Two particles interact by conservative forces.In addition, an external force acts on each particle.They complete round trips, ending at the points where they started.Which of the following must have the same values at the beginning and end of this trip?

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)=(8.0 J/m2)x2 + (2.0 J/m4)x4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s.It next stops momentarily to turn around at x =

A stationary mass m = 1.3 kg is hanging from a spring of spring constant k = 1200 N/m.You raise the mass a distance of 10 cm above its equilibrium position in a time of 1.4 s.What was the average power expended?

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below.They all start with the same speed and continue to move until brought to rest by friction.Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m3)x3.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

A stationary mass m = 1.3 kg is hanging from a spring of spring constant k = 1200 N/m.You raise the mass a distance of 10 cm above its equilibrium position.How much has the potential energy of the mass-spring system changed?

A small object slides along the frictionless loop-the-loop with a diameter of 3 m.What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)= (8.0 J/m2)x2 − (2.0 J/m4)x4.When the particle is at x = 1.0 m the magnitude of its acceleration is:

Objects A and B interact with each other via both conservative and nonconservative forces.Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the internal energy.If no external agent does work on the objects then:

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The potential energy of a particle moving along the x axis is given by U(x)= (8.0 J/m²)x² + (2.0 J/m⁴)x⁴. If the total mechanical energy is 9.0 J, the limits of motion are:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)=(8.0 J/m²)x²+ (2.0 J/m⁴)x^4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s.It next stops momentarily to turn around at x =

A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m³)x³.If the potential energy is taken to be zero for x = 0 then the potential energy is given by:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x)= (8.0 J/m²)x²− (2.0 J/m⁴)x⁴.When the particle is at x = 1.0 m the magnitude of its acceleration is:

Objects A and B interact with each other via both conservative and nonconservative forces.Let K_A and K_B be the kinetic energies, U be the potential energy, and E_int be the internal energy.If no external agent does work on the objects then: